Now you tell me!!!!!That is a FET it is not a transistor. All that stuff about how a transistor works is not relevant to your device. What is more your device requires 10V to turn it on. This is more than the arduino can supply so in general you can't use this device with the arrangement you have been looking for.So how did you identify the emitter base and collector on you device because it doesn't have them. It has a gate drain and source. So basically you have been lying when you say you have.

I was having a feeling that was a MOSFET. That will explain the transistor got hot. Kiss goodbye the LED. I hope the Arduino is still working. Why you simply use a 2N3904 or something like that ? No parts, right ?